Performance Measurement for Option Portfolios in a Stochastic Volatility Framework

40 Pages Posted: 7 Feb 2018 Last revised: 29 Nov 2019

See all articles by Rainer Baule

Rainer Baule

University of Hagen

Oliver Entrop

University of Passau

Sebastian Wessels

University of Hagen

Date Written: January 29, 2018

Abstract

Measuring the performance of stock portfolios that include options is challenging due to options' nonlinearity in the underlying, their exposure to volatility risk, and their time decay. Our contribution to the literature is twofold: First, we provide a theoretically rigorous derivation of the time-variable factor loadings in a two-factor model under stochastic volatility according to Heston (1993). Within this setting, the portfolio returns are explained by the market and an additional option factor, i.e., a portfolio of standard options exposed to volatility risk. We show that (i) any option factor is suitable to perfectly explain the portfolio behavior if simple returns are considered in instantaneous time and that (ii) the option factor's loading equals the fraction of the volatility elasticities of the portfolio and of the option factor while the option factor's underlying elasticity enters the factor loading of the underlying. Second, in applications however, time has to be discretized and factor loadings are usually estimated in a single regression over a certain time horizon, which regularly leads to a bias in performance measurement. We analytically show how the discretization error arises through nonlinearity related to both risk factors, the underlying and the volatility. We run a simulation analysis to analyze the size of this bias when different option factors from the common literature are used and propose a two-step procedure to keep the bias small.

Keywords: Performance Measurement, Option Portfolios, Stochastic Volatility, Heston, Nonlinearity, Volatility Risk, Option-Based Factors, Discrete Returns, Continuous Returns

JEL Classification: C13, C60, C61, C62, G10, G12

Suggested Citation

Baule, Rainer and Entrop, Oliver and Wessels, Sebastian, Performance Measurement for Option Portfolios in a Stochastic Volatility Framework (January 29, 2018). Available at SSRN: https://ssrn.com/abstract=3112675 or http://dx.doi.org/10.2139/ssrn.3112675

Rainer Baule

University of Hagen ( email )

Universitaetsstrasse 41
Hagen, 58097
Germany

Oliver Entrop

University of Passau ( email )

Innstrasse 27
Passau, 94032
Germany
+49 851 509 2460 (Phone)
+49 851 509 2462 (Fax)

Sebastian Wessels (Contact Author)

University of Hagen ( email )

Universitaetsstrasse 41
Hagen, 58097
Germany

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